Poker odds: outs, pot odds and hand probabilities, calculated

Key facts

Preflop: a pocket pair comes 1 in 17 hands, pocket aces 1 in 221, and two suited cards 23.5% of the time.
A pocket pair flops three of a kind or better 11.8% of the time (about 1 in 8.5), and two suited cards flop a flush draw 10.9% of the time.
With two cards to come, a flush draw (9 outs) gets there 35.0% of the time and an open-ended straight draw (8 outs) 31.5%. With one card to come it is 19.6% and 17.4%.
Pot odds: the equity you need to call is your call divided by the pot after your call. Facing a pot-sized bet you need 33.3%; facing a half-pot bet, 25%.
The rule of 4 overstates big draws: 15 outs is 54.1% by the river, not 60%.

Poker odds in two numbers

Every poker decision with a draw comes down to comparing two numbers. The first is your equity: the chance that your hand ends up best. The second is your pot odds: the share of the final pot you have to put in. If your equity is higher than the share you are paying, the call makes money over time; if not, it loses. Everything below is how to get both numbers quickly, with exact hold'em probabilities we calculated by counting every combination.

Preflop probabilities

Being dealt	Combinations of 1,326	Chance	About 1 in
A specific pair, e.g. A-A	6	0.45%	221
A-A or K-K	12	0.90%	111
Any pocket pair	78	5.88%	17
A-K, suited or not	16	1.21%	83
A-K suited	4	0.30%	332
Any two suited cards	312	23.5%	4.25
Two unpaired, offsuit cards	936	70.6%	1.4

Flop probabilities

Of the 19,600 possible flops for any two hole cards:

Your hole cards	What the flop gives you	Chance
Pocket pair	Three of a kind or better (a set)	11.8% (1 in 8.5)
Pocket pair	Four of a kind	0.24% (1 in 408)
Two suited cards	A made flush	0.84% (1 in 119)
Two suited cards	A flush draw (exactly two more of your suit)	10.9%
Two suited cards	A backdoor flush draw (exactly one more)	41.6%
Two unpaired cards	At least one card matching a hole card rank	32.4%
Connectors such as 8-9	A made straight	1.31% (1 in 77)

And by the river (all five community cards):

Starting hand	Finishes with	Chance
Pocket pair	Three of a kind or better from the pair	19.2%
Two suited cards	A flush using both hole cards' suit	6.4%

The second line is a useful reality check: suited cards make a flush only about once in sixteen hands, which is why "it's suited" is a weak reason to play a hand.

Outs: the poker odds table

Outs are the unseen cards that make your hand. On the flop there are 47 unseen cards (52 minus your two and the three on the board); on the turn, 46. The exact chance of hitting, compared with the popular rule of 2 and 4:

Outs	Next card (from the flop)	River only (from the turn)	Turn or river (from the flop)	Rule of 4	Rule of 2
1	2.1%	2.2%	4.3%	4%	2%
2	4.3%	4.3%	8.4%	8%	4%
3	6.4%	6.5%	12.5%	12%	6%
4	8.5%	8.7%	16.5%	16%	8%
5	10.6%	10.9%	20.4%	20%	10%
6	12.8%	13.0%	24.1%	24%	12%
7	14.9%	15.2%	27.8%	28%	14%
8	17.0%	17.4%	31.5%	32%	16%
9	19.1%	19.6%	35.0%	36%	18%
10	21.3%	21.7%	38.4%	40%	20%
12	25.5%	26.1%	45.0%	48%	24%
15	31.9%	32.6%	54.1%	60%	30%
18	38.3%	39.1%	62.4%	72%	36%
20	42.6%	43.5%	67.5%	80%	40%

The rule of 2 is close at every size. The rule of 4 is fine up to about 9 outs and then runs ahead of reality, by 6 points at 15 outs and 12.5 points at 20. If you use it on a monster draw, subtract a little.

Common draws and their outs:

Draw on the flop	Outs	Chance by the river
Gutshot straight draw (e.g. 9-8 on 7-5-2, needs a 6)	4	16.5%
Two overcards against a lower pair	6	24.1%
Open-ended straight draw	8	31.5%
Flush draw	9	35.0%
Flush draw plus open-ended straight draw	15	54.1%

Outs are an estimate, because some of them can also improve your opponent. An exact check: A♠ K♠ against Q♥ J♦ on a Q♠ 7♠ 2♦ flop looks like 15 outs (nine spades, three aces, three kings), suggesting 54.1%. Dealing out every turn and river gives the A-K 53.4%, a little lower, because a few runouts that hit the A-K also give the Q-J a better hand.

Pot odds: when a call is worth it

Pot odds turn the price of a call into the equity you need:

required equity = your call / (pot before your call + your call)

Here "pot before your call" includes your opponent's bet. Against the common bet sizes:

Opponent bets	You call to win	Pot odds	Equity you need
A quarter of the pot	1 to win 5	5 to 1	16.7%
A third of the pot	1 to win 4	4 to 1	20.0%
Half the pot	1 to win 3	3 to 1	25.0%
Two thirds of the pot	1 to win 2.5	2.5 to 1	28.6%
The size of the pot	1 to win 2	2 to 1	33.3%
Twice the pot	1 to win 1.5	1.5 to 1	40.0%

Worked example. On the turn you hold a flush draw: 9 outs, one card to come, 19.6%. The pot is $60 and your opponent bets $30. You must call $30 into a pot that will be $120, so you need 25%. With 19.6% the call loses money unless you expect to win more on the river when you hit (implied odds). Change one thing: the same draw on the flop with your opponent all in, so you see both cards. Now your chance is 35.0%, comfortably more than 25%, and the call is right.

This is an expected value calculation in disguise: 19.6% x $120 = $23.52 back for a $30 call, an average loss of $6.48. Our calculator does the same sum for any bet.

Pundit tip: in a casino cash game, the commission comes out of the pot you are drawing to. Do your pot odds on what you will actually be paid after rake, not the gross pot.

Where these odds apply

The tables above are for Texas hold'em; the full rules are in our texas holdem rules guide, and starting hand match-ups are there too. In omaha poker you hold four cards, so draws are bigger and the rule of 4 overstates them even more often. For the probability of every five and seven card hand, see poker hand rankings.

Knowing the odds does not change one thing: against the house, as in video poker or casino table games, the maths is fixed against you; against other players, the rake is. Online real money poker cannot legally be offered to people in Australia under the Interactive Gambling Act 2001, which our online poker Australia page covers. If the numbers stop adding up for you, free help is on our gambling help australia page.

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Frequently asked questions

How do you calculate poker odds?

Count your outs, the unseen cards that would give you the best hand. With one card to come your chance is outs divided by the unseen cards (46 on the turn, 47 on the flop for the next card). With two cards to come it is 1 minus the chance of missing twice: 1 - (47 - outs)/47 x (46 - outs)/46.

What are pot odds?

The price of a call compared with what you can win. If the pot is $100 and your opponent bets $50, you call $50 to win a pot of $200, so you need to win at least $50 / $200 = 25% of the time for the call to break even.

What is the rule of 2 and 4?

A shortcut: multiply your outs by 4 on the flop (two cards to come) or by 2 on the turn (one card to come) to estimate your percentage. It works well for small draws but overstates big ones; 15 outs gives 60% by the rule against 54.1% exactly.

What are the odds of being dealt pocket aces?

6 combinations out of 1,326, or 1 in 221 hands (0.45%). Any pocket pair is 78 combinations, or 1 in 17 hands.

What are the odds of flopping a set with a pocket pair?

11.8%, about 1 in 8.5 flops, which includes the rare flop of four of a kind. By the river, a pocket pair improves to three of a kind or better 19.2% of the time.